Minimizing pressure sensitivity of optical fibers is important where they are used as lead and as reference fibers to phase modulated, interferometric sensors. In optical fiber acoustic sensors it is desirable to localize the fiber sensitivity by making the lead optical fibers pressure insensitive. In other optical fiber sensors (e.g., temperature and magnetic), it is desirable to desensitize the fiber including even the sensing area to acoustic wave pressure because such acts as a noise source. It is important to localize the fiber sensitivity to a desired area.
In general, the sensitivity of an optical fiber is a complicated function of the elastic and elasto-optic coefficients of the optical fiber, the elastic coefficient of the coating and the thickness of the various fiber layers. The pressure sensitivity of the optical phase in a fiber is defined as .DELTA..phi./.phi..DELTA.P, where .DELTA..phi. is the shift in the optical phase delay .phi. due to a pressure change P. If a given pressure change, .DELTA.P, results in a fiber core axial strain .epsilon..sub.z and radial strain .epsilon..sub.r, then it can be shown that (see N. Lagakos and J. A. Bucaro, "Pressure Desensitization of Optical Fibers," Appl. Opt. 20, 2716 (1981)): ##EQU1## Here P.sub.11 and P.sub.12 are the elasto-optic coefficients of the core and n is the refractive index of the core. The first term in Eq. (1) is the part of .DELTA..phi./.phi..DELTA.P which is due to the fiber length change, while the second and third terms are the parts due to the refractive index modulation of the core, which is related to the photoelastic effect. In order to calculate the sensitivity as given by Eq. (1), the strains in the cores .epsilon..sub.z and .epsilon..sub.r must be related to properties of the various layers of the fiber. The various constants involved in these calculations are found from the appropriate boundary conditions. The details of this analysis have been reported in "Pressure Desensitization of Optical fibers," by N. Lagakas and J. A. Bucaro, Appl. Opt. 20, 2716 (1981).
As can be seen from Eq. (1), the sensitivity of an optical fiber is related to the combined effects of pressure induced fiber length changes and strain induced index of refraction effects. For low frequencies where pressure is hydrostatic, these effects are generally of opposite polarity. Accordingly, pressure insensitivity can be achieved by balancing these effects. In particular, it is possible to achieve this by designing fibers consisting of a glass core with a relatively low bulk modulus and a glass substrate with a high bulk modulus. The glass fiber can then be coated in the usual way, first with a soft rubber and then with a hard plastic. Pressure insensitive fibers can also be achieved by applying a high bulk modulus glass substrate or metal coating to conventional fibers.
High frequency acoustic fields, however, generate radial strains only. In this case, the axial strain .epsilon..sub.z, becomes zero. There is no proposed way of making optical fibers with reduced pressure phase sensitivity to radial strains only.